Q. 36 B5.0( 1 Vote )

Find one-parameter families of solution curves of the following differential equations:


Answer :


Given



This is a first order linear differential equation of the form



Here, P = –1 and Q = cos 2x


The integrating factor (I.F) of this differential equation is,





We have


I.F = e–x


Hence, the solution of the differential equation is,






Let












5I = e–x(2 sin 2x – cos 2x)



By substituting the value of I in the original integral, we get





Thus, the solution of the given differential equation is


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